Related papers: The work of James Maynard
For polynomials of degree two over finite fields, we present an improvement of Fitzgerald's characterization (Finite Fields Appl. 9(1):117-121, 2003). We then use this new characterization to obtain an explicit, complete, and simple…
In this article we give a Drinfeld modular interpretation for various towers of function fields meeting Zink's bound.
Manifolds have uses throughout and beyond Mathematics and it is not surprising that topologists have expended a huge effort in trying to understand them. In this article we are particularly interested in the question: `when is a manifold…
The following paragraphs will describe the origins of John Rainwater, the impact of his work, the motivations for various parts of it and the prospects for his future.
We propose a way to encode acceleration directly into quantum fields, establishing a new class of fields. Accelerated quantum fields, as we have named them, have some very interesting properties. The most important is that they provide a…
As a corollary to the recent extraordinary theorem of Maynard and Tao, we re-prove, in a stronger form, a result of Shiu concerning "strings" of consecutive, congruent primes.
A degree of a module $M$ is a numerical measure of information carried by $M$. We highlight some of Vasconcelos' outstanding contributions to the theory of degrees, bridging commutative algebra and computational algebra. We present several…
Several questions of scientometrics parameters organization are considered. Two new indices for scientific works citation analysis are proposed. They provide more detailed and reliable scientific significance assessment of individual…
I discuss the general principles underlying quantum field theory, and attempt to identify its most profound consequences. The deepest of these consequences result from the infinite number of degrees of freedom invoked to implement locality.…
This is a popular article about the work of Maryna Viazovska, 2022 Fields medalist.
We follow some (wild) speculations on trying to understand the uniqueness of our physical world, from the field concept to F-Theory.
I review and discuss a selected sample of recent results in pNRQCD.
Planck introduced his famous units of mass, length and time a hundred years ago. The many interesting facets of the Planck mass and length are explored. The Planck mass ubiquitously occurs in astrophysics, cosmology, quantum gravity, string…
Following ideas given by John Bell in a paper entitled \textit{Beables for quantum field theory}, we show that it is possible to obtain a realistic and deterministic interpretation of any quantum field-theoretic model involving Fermi…
What science does, what science could do, and how to make science work? If we want to know the answers to these questions, we need to be able to uncover the mechanisms of science, going beyond metrics that are easily collectible and…
We survey the classical results on the prime number theorem
This is an article for a general mathematical audience on the author's work, joint with Terence Tao, establishing that there are arbitrarily long arithmetic progressions of primes. It is based on several one hour lectures, chiefly given at…
Random matrices now play a role in many parts of computational mathematics. To advance these applications, it is desirable to have tools that are flexible, easy to use, and powerful. Over the last 25 years, researchers have developed a…
This is an introduction to some recent developments in string theory and M theory. We try to concentrate on the main physical aspects, and often leave more technical details to the original literature.
In the scientific literature the equation $Q=\{Q\}[Q]$ is frequently quoted, where $Q$ denotes a quantity, $\{Q\}$ a numerical value, and $[Q]$ a unit. During the last years some experts claimed, that this equation is due to James Clerk…